I feed my two girls together. But I stand right in the middle to make sure each stays away from the others bowl. If they don't eat it while it is down, it gets taken up. You will be surprised how fast they pick up on this. This has worked for us. I have never had to put them in separate rooms. But like I said, I stay right there with them. After the food was taken up a time or two they learned to eat it while it is there.
